C0NF-920913--3
DE93 001705
DIMENSIONLESS SCALING OF CONFINEMENT IN ATF*
M. MURAKAMI, T.S. BIGELOW, J.B. WILGEN, R.A. DORY, B.A. CARRERAS, S.C. ACETO1, D.B. BATCHELOR, L.R. BAYLOR, G.L. BELL, J.D. BELL, RJ. COLCHIN, E.C. CRUME, N. DOMINGUEZ, J.L. DUNLAP, G.R. DYER, A.C. ENGLAND, R.F. GANDY2, J.C. GLOWIENKA, R.C. GOLDFINGER, R.H. GOULDING, G.R. HANSON3, J.H. HARRIS, S. HIROE, S.P. HIRSHMAN, L.D. HORTON4, H.C. HOWE, D.P. HUTCHINSON, R.C. ISLER, T.C. JERNIGAN, H. JI*, H. KANEKO*, M. KWON^, R.A. LANGLEY, D.K. LEE, K.M. LIKIN?, J.F. LYON, C.H. MA, M.M. MENON, O. MOTOHMA*, H. OKADA«, S. PAUL*, A.L. QUALLS3, D.A. RASMUSSEN, R.K. RICHARDS, J.A. ROME, MJ. SALTMARSH, M. SATO*, J.G. SCHWELBERGER*. K.C. SHAING, M.G. SHATS?, T.D. SHEPARD, J.E. SIMPKINS, C.E. THOMAS, T. UCKAN, K.L. VANDER SLUIS, M.R. WADE3, W.R. WING, H. YAMADA*. JJ. ZIELINSKI*
Oak Ridge National Laboratory Oak Ridge, Tennessee M . United States of America
•Research sponsored by the Office of Fusion Energy, U.S. Department of Energy, under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc.
^enssclaer Polytechnic Institute, Troy, NY 12181, USA. 2Auburn University, Auburn. AL 36849, USA. 3Oak Ridge Institute for Science and Education, Oak Ridge, TO 37831, USA. 4JET Joint Undertaking, Abingdon, England. ^National Institute for Fusion Science, Nagoya, Japan. ^University of Texas at Austin, Austin, TX 78712, USA. ^Institute of General Physics of the Academy of Sciences, Moscow, Russian Federation. 8PIasma Physics Laboratory, Kyoto University, Uji, Japan. Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA.
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DISTRIBUTJOW OF THIS DOCUMENT IS UNLIMITED ABSTRACT. The results of dimensionless-parameter modulation and con- figuration control experiments in the Advanced Toroidal Facility (ATF) are pre- sented. The global energy confinement time fits gyro-Bohm scaling better than Bohm-likc scaling. An additional dependence was determined by modulation of single dimensionless parameters (collisionality v* and beta P), yielding TE^gB ocVl(iavpapt where av = 0.18 ± 0.03 and ap = 0.3 ± 0.1. Application of this formula to NBI and ECH data significantly improves the fit, implying that improved confinement will result from increasing the heating power. Little change in confinement occurred for wide variations in the confined trapped par- ticle fraction at constant magnetic well radius and shear. This may be explained by reduction of the helically trapped particle loss region due to the radial electric field. Configuration modulation experiments showed that the energy confinement time improves as the magnetic well radius expands, the result expected from some stabilization of resistive interchange instabilities. This is consistent with fluctuationmeasurement s and may explain the positive dependence of confinement on p.
1. INTRODUCTION The Advanced Toroidal Facility (ATF) was designed to investigate improve- ment of toroidal confinement concepts in a stellarator device. The device [1,2] is an & = 2, m = 12 sheared stellarator (torsatron) with major radius Rn of 2.1 m, average minor radius a of 0.27 m, and maximum magnetic field on axis Bo of 2 T. In the standard configuration, the rotational transform * (»1/q) varies from 0.3 on the axis to 1.0 at the edge, and a modest magnetic well extends out to about the + = 1/2 surface at the normalized radius (p * T/a) of -0.6. The earlier studies used up to 1.5 MW of neutral beam injection (NBI) from two opposing tangential 40 kV, 0.3 s injectors. The plasma performance in this device is similar to that in a tokamak of the same minor radius (e.g. ISX-B) [2,3]. The maximum parameters achieved (not simultaneously) are Tj(O) -1.0 keV, T$(0) • 20 1.5 keV, ne » 1.5 x 10 ur\ XE ~ 30 ms, and
2. DIMENSIONLESS SCALING EXPERIMENTS Confinement time in a toroidal device is described in dimensionless param- eters [8-12],
-2- where TE is the energy confinement time, Cl is the gyrofrequcncy, p* is the ratio of the gyroradius (ps) to the average plasma radius (a"), v* is the collisionality, and P is the plasma beta. The coefficient C can be a function of other dimension- less parameters, including those related to magnetic configurations, as discussed later. We first focus on the dependence of the first three variables in a fixed (standard) configuration. The leading term (p* dependence) can be compared with two limiting forms: Bohm-like (ctp » 2) and gyro-Bohm-like (Op * 3) scaling, which are characterized by long-wavelength (of scale a) and short- wavelength (of scale ps) turbulence, respectively. Any remaining v* and P dependence can help explain the source of the turbulence by comparison with theoretical scaling [12]. The earlier regression analyses [3] of the global energy confinement time TE in ATF were made from data in a multishot database representing diverse conditions with both NBI and ECH plasmas. These suggested that the gyro- Bohm scaling was more closely followed than the Bohm-like scaling, although the distinction was not strong (Table II). We also observed that the LHD empirical expression [13] based on past stellarator data agrees well with the gyro-Bohm scaling [10]. Regression analysis of the ATF data for the above dimensionless form yields the exponents Op = -3.1 (with additional exponents of av = -0.45 and ap = 40.83), indicative of gyro-Bohm-like scaling. However, coUinearity of the control variables and the presence of hidden variables (e.g. heating power profile shape) make the distinction less certain. Since gyro-Bohm scaling gives the leading term variation, the more recent experiment was aimed at determining the additional dependence of v* and P in the standard magnetic geometry (with a fixed coefficient Q. The experiment involved modulation of a single dimensionless variable (v* or p) while keeping the other constant This was accomplished by simultaneously modulating ECH power P and electron density (with gas feedback) such that &7n * (-2/3)P/P for v* modulation and nVn * (4/9)P/P for P modulation, where both equations are based on the gyro-Bohm scaling. Figure 1 shows the time evolution of the plasma parameters in the v* modulation. For a given ECH power modulation (P/P - 25%), the amplitude and phase of the density feedback demand were adjusted to give the specified line-average density modulation (ftTn « 15%). The modulation period (80 ms) was chosen to be longer than both energy and particle confinement times, and the modulation was applied (at 0.16 s) after the quasi- stationary discharge was established The polar diagram in Fig. 2 shows relative modulation amplitudes and phases of several global (magnetic-based) and local (at a radius of p = 0.64 in the confinement region) plasma parameters based on Fourier analysis at the modulation frequency (12.5 Hz). A modulation amplitude of 50% in v* with a negligible -3- out of phase) {12]. This may imply that the global scaling derived is representative of local phenomena in the confinement region (p - 2/3). Regression analysis for both this V* scan and the orthogonal j} scan yields ccv = -0.18 and ap = +0.36 for the modification to the gyro-Bohm scaling. Since regression of tg/'CgB in the overall ATF database (which includes data with NBI) yields av = -0.17 and ap = +0.31, we conclude that ocv = -0.18 ± 0.03. Based on this v* dependence, Fig. 3 shows variation of the exponent ap as a function of (P) in the overall database, indicating ap = 0.3 ± 0.1 over the range of (P) up to 1.7%. Use of both the v* and p dependences significantly improves the fit over the ordinary gyro-Bohm scaling, as shown in Fig. 4. Of the theoretical models compared with tokamak data in Ref. [12], dissipative trapped electron mode (DTEM) models (developed for tokamaks) give an opposite dependence on v* (av - +0.4), implying that DTEM may not play a significant role in global confinement in these ATF experiments. A simple tokamak-based resistive MHD turbulence model shows that the v* dependence is close to the data (av = -0.4), but the P dependence is opposite. The indicated favorable trend of confinement with increasing 0 may result from the p* self- stabilization effect on interchange modes [14], as discussed below. Though the range over which this scaling can be extrapolated is uncertain, it suggests excellent prospects for improved confinement in ATF with increased heating power, since adding power both increases p and decreases collisionality. 3. MAGNETIC CONFIGURATION SCANS The flexible magnetic configuration control in ATF allows independent control of parameters that are fundamental to toroidal confinement and stellarator optimization [1]. The three degrees of freedom afforded by the three vertical field coil sets enable us to prescribe the dipolc and quadrupole moments (specifying the magnetic axis shift and plasma shaping, respectively) while the linked flux is kept constant (to avoid driving an inductive current). The variation of the poloidal field permits external control of physical properties of magnetic confine- ment on a flux surface, such as magnetic field curvature (and thus control of magnetic well and hill), rotational transform (shear), and IB I spectrum (neo- classical viscosity) and trapped particle population. Figure 5 shows contour plots of three configuration-related (dimensionless) parameters in the dipole- quadrupole configuration space: (1) contained trapped particle fraction frrc, which is related to the helically trapped particle loss region modeled without the electric field; (2) average magnetic shear, s = -(p/+)(d-t/dp) at normalized radii p between 0.4 and 0.6; and (3) magnetic well radius P\r*o inside which the mag- netic well resides for low-P plasmas (($) = 0.1%, typical for ECH plasmas). Contours of constant magnetic shear and well radius nearly coincide for these low-P plasmas, but contours of constant frpc arc nearly orthogonal to the other two over much of the range of interest This enables separating the effects of the trapped particle population from those of magnetic shear and well/hill. A full-range dynamic variation (along path 1 in Fig. 5) of the parameter fjpc was accomplished with two long-pulse discharges while keeping constant the -4- shear and magnetic well and the line-average electron density (by density feed- back control). Figure 6 shows results of such a scan. Changing fjpc nas little effect on plasma parameters until this quantity becomes greater than 0.8. Although the ECH power deposition profile changes somewhat with increasing fxpo the deposition profiles tend to remain broad and rather insensitive to the variation of the configuration (except possibly for the extreme value of frpc) with the present ECH launching scheme [4]. One possible explanation for the insensitivity of the confinement is me radial electric field that tends to reduce the orbit loss region. Heavy ion beam probe (HIBP) measurements of plasma poten- tial in configurations other than the standard one are rather sparse, but data are available for a quadrupole scan (path 2 in Fig. 5) [15]. Figure 7 shows that the electric field measured by the HIBP increases as the loss region expands (i.e. as frpc decreases) in this scan. The simultaneous increase in the global energy con- finement time in the quadrupole scan may hint at an improvement of confinement with increasing radial electric field, as seen in the L-H transition in tokamaks. The role of the electric field in reducing the loss region is important for stellarator optimization, so further studies are clearly needed. Implications of this scan related to the DTEM instability are discussed in the companion paper [16]. Figure 8 shows the plasma response to sinusoidal modulation (along path 3 in Fig. 5) of the magnetic well radius. The modulation substantially affects the stored energy and core electron temperature. This result is consistent with resistive interchange modes influencing energy confinement, since interchange modes are stabilized by a magnetic well. Density fluctuation measurements showed radial behavior of Wn consistent with theoretical predictions of resistive interchange modes [13]. Difficulties in separating the effects of magnetic shear and well/hill can be mitigated by magnetic well broadening in higher-p plasmas. Indeed, the earlier experiments with centrally peaked pressure profiles (due to field errors) showed suppression of interchange modes at relatively low P (Po £ 1.5%), consistent with theoretically predicted p self-stabilization [16]. 4. CONCLUSIONS The favorable v* and P dependences (ccv = -0.18 ± 0.03, ap = 0.3 ±0.1) experimentally observed suggest excellent prospects for improved confinement in ATF with increased heating power. Long-pulse and modulation techniques have been used to establish the dependence of confinement on critical stability factors: magnetic shear, well/hill, and trapped particle fraction. It is anticipated that at some time in the future these experiments will be extended to higher heating power to provide useful information on stellarator optimization and a better understanding of toroidal transport ACKNOWLEDGEMENTS We acknowledge with appreciation the contributions of many members of the ATF group, in particular, G.H. Henkel, L.A. Massengill, T.F. Rayburn, C.R. Schaich and J.L. Yarber for operational support; J.A. White for -5- engineering; J.M. Gossett, G.L. King and T.M. Raybum for diagnostic measurements; and D.C. Giles, D. E. Greenwood, K.L. Kannan, D.R. Overbey and T.C. Patrick for data handling. We also thank C.H. Johnson and M.B. Nestor for publication assistance, F.W. Perkins (Princeton Plasma Physics Laboratory) for stimulating discussions, and J. Sheffield and W. Fulkerson for encouragement and continuous support This research was sponsored by the Office of Fusion Energy, U.S. Department of Energy, under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. REFERENCES [1] LYON. J.F., CARRERAS. B.A.. CHIPLEY, K.K., el al.. Fusion Technol. 10 (1986) 179. [2] MURAKAMI, M., ACETO, S.C., ANABITARTE, E., et al., in Plasma Physics and Controlled Fusion Research (Proc. 13th Int. Conf. Washington. DC, 1990) IAEA, Vienna. Vol. 2 (1991) 455. [3] DORY, R.A., MURAKAMI, M., WING, W.R., ATF Team, Comments Plasma Phys. Controlled Fusion 14 (1991) 237. [4] MURAKAMI, M., ACETO, S.C.. ANABITARTE, E., et al., Phys. Fluids B 3 (1991) 2261. [5] RICHARDS, R.K., HUTCHINSON. D.P., et al., to be published. [6] MURAKAMI, M., BIGELOW, T.S.. GOLDFINGER, R.C., et al., in Radio Frequency Power in Plasmas (Proc. 9th Top. Conf. Charleston, 1991) American Institute of Physics, New York (1992) 3 (AD? Conf. Proc. 244 (1992) 3]. [7] ISLER, R.C., ACETO, S.C., BAYLOR, L.R., et al., Phys. Fluids B 4 (1992) 2104. [8] KADOMTSEV, B.B., Sov. J. Plasma Phys. 1 (1975) 295. [9] CONNOR, J.W., TAYLOR. J.B.. Nucl. Fusion 17 (1977) 1047; CONNOR, J.W., Plasma Phys. Controlled Fusion 30 (19S8) 619. [10] PERKINS, F.W., Issues in Tokamak/Stellarator Transport and Confinement Enhance- ment Mechanisms, Rep. PPPL-2708, Plasma Physics Laboratory, Princeton, New Jersey (1990). [11] WALTZ, R.E.. et al., Phys. Rev. Lett. 65 (1990) 2390. [12] CHRISTIANSEN, J.P., et al., Nucl. Fusion 30 (1990) 3635. [13] SUDO, S., et al.. Nucl. Fusion 30 (1990) 1352. [14] CARRERAS. B.A.. Comments Plasma Phys. Controlled Fusion 12 (1988) 35. [13] HARRIS, J.H., et aL, Fluctuation Studies in ATF, IAEA-CN-56/C-1-3, this conference. [15] ACETO, S.C., et al., to be published. [16] HARRIS, J.H.. MURAKAMI, M., CARRERAS. B.A., et al.. Phys. Rev. Lett. 63 (1989) 1253. -6- TABLE I. ATF PARAMETERS FOR FOUR DIFFERENT OPERATING REGIMES Regime High stored LongECH energy High (3 Low v* pulse Shot number 11740 11186 14514 16654 BoCD 1.9 0.45 1.9 0.95 nc (1019 m-3> 11 4.3 0.53 0.5 P(MW) 0.96 0.98 0.79 0.25 TE (ms) 26 6.1 6.4 5.0 Tco(keV) 0.4 0.3 1.0 1.0 Tio(keV) 0.4 0.3 1.0 0.2 (P) (%) 0.4 1.7 0.1 0.15 Duration (s) 0.25 0.2 0.15 20 TABLE H. COEFFICIENTS AND STATISTICS FOR SCALING LAW FITS FOR GLOBAL ENERGY CONFINEMENT TIME ota TE (s) - C • n2o • BT°B • Scaling Constant On OB -7- SHOT 19671 B- 0.96 T 400 I 1 1 1 1.0 . PECH lA '"\A ' I - 200 \ / n. - 0.5 t I n 1 1 1 1 1 1 1 0.6 1 i 1 1 AIA n AIK ' t \ \\ 1 i / 1 / I I / 1 ; 0.3 ~ / v 0.1 g * 1 i vy i / — v A / V / I / \J \\J / \ -0.64)V i 1 I 1 1 1 0 i 1 1 1 1 20 J i 'XE /~\T0B/ \ / - v\t 1 t V ^E i 1 1 1 1 i 0.4 0.6 0.8 TIME(») FIG. 1. Time evolution of plasma parameters with v* modulation and constant SHOT NO. 19671 FIG. 2. Polar diagram of the relative modulation of global (shown by bold arrows) and local (fine arrows) plasma parameters for the v* scan. -8- FIG. 3. Development of the dependence of confinement time using the ATF database with Oy = -0.18. 2 R2-0.952 o >^ R «0S87 o >/^ 0.03 ' o2-4^9% o S 2 0.02 0.01 «BP*^2F » ECH J|^ « ECH JP" O NBI >flP^ o NBi OJ02 0.03 0 0J01 OJO2 0.03 OJB55T0B(S) FIG. 4. Comparison of gyro-Bohm scaling and its modification in fitting experimental energy confinement times. The gyro-Bohm expression is given by 0 6 0 6 2244 06 TgB (s) = 0.25 • BT°« • n2o - • PMW" - • am • °* -9- Fraction of trapped particle* confined: frpc Magnetic shear: s > -iP'<){ /< / 1 si WPOLE MOMENT,-AQ io FIG. 5. Contour plots of physics parameters in the dipole-quadrupole configuration space and paths followed in the dynamic configuration scans. 2.0 1.0 1 I |^|-0.62 ±0.02 Pv«-o- 0.59 ±0.01 ? a o 1.0 I I J_ 0.4 0.6 0.8 1.0 FRACTION OF TRAPPED PARTICLES CONFINED, frpc FIG. 6. Plasma parameters as a function of the confined trapped particle fraction during a dynamic configuration scan in which the well radius and the shear are kept constant -10- 1.0 0.8 0.6J 0.4 0.2 -0.04 FIG. 7. Variations of measured electric potential (O at p = 0.6 relative to the plasma edge), confined trapped particle fraction, and global energy confinement time in a quadrupole scan. B-0.96T SHOT 18291 0.70 0.70 0.45 0.45 0.8 1.6 E 0.8 0.4 U-n, \r* v- V- I I I I I I 1.0 3.0 I °-5 FIG. 8. Time evolution of plasma parameters with sinusoidal modulation of the magnetic well radius and constant contained trapped particle fraction. -11-